In the criminal case, the burden of proof rests solely on the government. The defense need make no defense whatsoever beyond merely denying the charges.

That's the theory, but it practice it is the opposite. I was on a petit jury once and the (court-appointed) defense attorney made just that point: he offered no evidence on behalf of the defendant, and asked no questions about any testimony offered by the prosecution. He said he needed to present no defense, that the burden of proof was on the prosecution.

This did not go well with the jury. IMAO, the defense attorney should have been disbarred. It is my view that the prosecution did not make a case. It was logically faulty. But the other jurors voted to convict after a few minutes. Since the prosecution's logic was so faulty, I held out for acquittal for a week, but, to my shame, eventually gave in.